设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.

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设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.设Sn是

设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.
设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.

设Sn是等差数列{an}的前n项和,已知S8=108,Sn=630,S(n-8)=234,求n.
a(n-7)+a(n-6)+a(n-5)+······+an=Sn-S(n-8)
=630-234
=396 (1)
a8 + a7 + a6 +……+ a1 = S8 =108 （2）
1式加2式可得：
[a(n-7)+a8] + [a(n-6)+a7] + ······+（an+a1) =396+108
8(an+a1) =504
an+a1 = 63 (根据若m+n=p+q,则 am+an = ap+aq)
Sn=(a1+an)n/2
630=63n/2
n=20

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